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THE brutal gang rape and murder of a college student last December and last week’s rape of a 5-year-old girl remind us that economic growth has not necessarily empowered women in India.

According to the Indian National Crime Bureau, 24,206 cases of rape were reported in 2011, or one every 21 minutes. Only 26 percent of these cases resulted in conviction, a 0.2 percent decline from 2010. Domestic abuse also remains a serious problem. The World Bank reports that in India, 47 percent of women were physically abused by their husbands in 2006, 21 percent of whom were beaten for simply “burning the food” and 31 percent for “arguing.”

Indian women have higher illiteracy rates than men (26 percent versus 12 percent, respectively, among those ages 15 to 24), and dramatically lower levels of labor force participation (29 percent versus 81 percent for those 15 and older in 2010).

These statistics are startling, especially when one considers that India is the world’s largest democracy and has experienced considerable gains in economic prosperity. Indeed, India’s per capita gross domestic product, adjusted for purchasing-power parity (an estimate of average annual income), has more than doubled since 2000 and more than quadrupled since 1990. Real GDP growth demonstrates similar gains, averaging 7.3 percent from 2000 to 2010.

The disparities between economic growth and gender rights are not unique to India. Nor are they limited to certain political systems. Writers Nicholas D. Kristof and Sheryl WuDunn highlighted the problem of missing girls, 30 million in China alone. Egypt’s Muslim Brotherhood objects to the proposed U.N. declaration that seeks equal inheritance, full equality in marriage and an abolition of the need for a husband’s consent to work, travel and use contraception.

So what explains the missing link between economic development and gender equality?

One view is that development should promote equality because the adoption of labor-saving technologies means that women can spend less time tending the household and more time developing marketable skills and seeking employment. Families should possess greater incentive to invest in their daughters’ education so they can generate income in the future. These increases in human capital elevate costs for employers who hold on to discriminatory labor policies. Development should also advance equality among husbands and wives. As a woman’s capacity to earn rises, so too should her bargaining power within the household, which can promote female empowerment.

Yet, our recent analysis demonstrates that the actual dynamics are more complex. We find that the relationship between gender equality and development can vary across different phases of development. We term this “the Gender Kuznets Curve.”

In the early stages of growth, up to an estimated $8,000 to $10,000 GDP per capita across cases, economic gains improve gender equality, particularly in the labor force. These gains also confer greater social and political rights, as women increase political participation, achieve occupational power and independent revenue and expand social networks.

Regrettably, these gains are not open-ended. As development advances further, prosperity creates a backlash. Patriarchal institutions and reactionary forces, threatened by female empowerment, respond with attempts to roll back progress. Sexual discrimination in the labor force and diverging male and female incomes decrease the opportunity costs for women to remain in the home. Calls from status quo beneficiaries to return to so-called traditional values lend traction to social norms that stigmatize men with employed wives.

The backlash also reinforces cultural values that favor male over female children. For example, scholars find that abortions of female fetuses tend to increase with prosperity because male children confer greater social status. Indeed, according to the 2011 Indian census, unfavorable sex ratios are more common in richer areas such as Delhi (866 women per 1,000 men), Punjab (893 to 1,000) and Haryana (877 to 1,000).

Fortunately, as development progresses further, this trend should reverse. We estimate this threshold to be approximately $25,000 to $30,000 in per capita gain.

Young girls continue to attend school, which enhances their human capital and the future value of labor force participation. Over time, these investments again increase the opportunity costs for women to remain at home and arguments that support male dominance diminish with the potential to achieve greater income gains. Enhanced female visibility in society and economic power can weaken discriminatory institutions, which can advance women’s political and social power and facilitate a push toward greater equality.

The categories we estimate are not written in stone and the thresholds are not magic bullets. They reflect policy choices and social customs. Instead of waiting for economic growth to further gender equality, governments and societies can adopt concrete measures to counter the backlash that pervades the second stage of the developmental process.

India’s 108th Amendment Bill, which mandates a 33 percent reservation for women in all legislative bodies, is a case in point. This bill is currently stalled in the Indian Parliament. Were the bill to be enacted, it could create new opportunities for women to occupy positions of power and authority, which should help to discourage discrimination across Indian society.

Crimes against women need to be punished severely. Following the Delhi rape case, a committee headed by former Indian Supreme Court Chief Justice J.S. Verma was formed to recommend changes to the Indian criminal code. The committee’s report calls for, among other things, stricter rape penalties and greater enforcement of existing laws. This is an important step, one that the Indian government would be wise to heed.

Joshua Eastin, left, is a Ph.D. candidate in political science at the University of Washington. Aseem Prakash is a political-science professor and the Walker Family Professor for the UW College of Arts and Sciences.